The high-power narrow-linewidth fiber laser has become the most widely used high-power laser source nowadays. Further breakthroughs of the output power depend on comprehensive optimization of stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS) and transverse mode instability (TMI). In this work, we aim to further surpass the power record of all-fiberized and narrow-linewidth fiber amplifiers with near-diffraction-limited (NDL) beam quality. SBS is suppressed by white-noise-signal modulation of a single-frequency seed. In particular, the refractive index of the large-mode-area active fiber in the main amplifier is controlled and fabricated, which could simultaneously increase the effective mode field area of the fundamental mode and the loss coefficient of higher-order modes for balancing SRS and TMI. Subsequent experimental measurements demonstrate a 7.03 kW narrow-linewidth fiber laser with a signal-to-noise ratio of 31.4 dB and beam quality factors of Mx2 = 1.26, My2 = 1.25. To the best of our knowledge, this is the highest reported power with NDL beam quality based on a directly laser-diode-pumped and all-fiberized format, especially with narrow-linewidth spectral emission.